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As one of the new roller coaster engineers, you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the roller coaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the roller coaster crosses the x–axis. Precise measurements and attention to detail are very important.
coordinate plane with buildings blocking off x–intercepts of negative 11, negative 10, 0, 1, 2, 3, 9, and 10
First, here is the existing map of current structures. It is important that the roller coaster does not go through the foundation of any of these structures.
1st point: ___6___
3rd point: ___-7___
1.Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your roller coaster. Show all of your work.
2.Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences.
3.Solve for the y–intercept for your function, f(x), and then construct a rough graph of your roller coaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.